Question

In triangle ABC, D is the mid-point of side AC such that BD = ½ AC. Show that ABC is a right angle

Answer 1

Answer:

From the figure we know that D is the midpoint of the line AC So we get AD = CD = ½ AC It is given that BD = ½ AC

So we can write it as

AD = BD = CD

Let us consider AD = BD

We know that the angles opposite to equal sides are equal

So we get ∠ BAD = ∠ ABD …..(1)

Let us consider CD = BD

We know that the angles opposite to equal sides

are equal So we get ∠ BCD = ∠ CBD ….. (2)

By considering the angle sum property in △ ABC We get ∠ ABC + ∠ BAC + ∠ BCA = 180o

So we can write it as ∠ ABC + ∠ BAD + ∠ BCD = 180⁰

By using equation (1) and (2)

we get ∠ ABC + ∠ ABD + ∠ CBD = 180⁰

So we get ∠ ABC + ∠ ABC = 180⁰

By addition 2

∠ABC = 180⁰

By division

∠ABC = 90⁰

Therefore, ABC is a right angle.

Hope it helps you.....